The master thesis at hand addresses time-optimal planning of trajectories for a flexible link. The goal is to convey this dynamic system, in compliance with certain restrictions, from one equilibrium into another in the shortest possible time. Initially, an infinite-dimensional mathematical model is created for this distributed- parameter system, which is subsequently simplified into a finite-dimensional linear approximation model. The main part is made up by the construction of time-optimal trajectories with two different approaches. Both methods, the given dynamic optimization task is being gradually simplified to a static one. Due to the linearity of the system, it is particularly easy to determine its sampling system, which is first used to formulate a suitable static optimization problem. The industrial partner suggested that a flatness-based method of trajectory planning will be developed additionally. By incorporating the flat output into the dynamic optimization task and a appropriate parameterization of it, the given task can again be expressed by a static optimization problem. The comparison of the advantages and the quality of the solutions of both of the methods is prioritized here. Finally, the practical applicability of the planned trajectories should be investigated by means of experiments on the fair demonstrator.